2012
DOI: 10.2206/kyushujm.66.303
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MOTION AND B^|^Auml;CKLUND TRANSFORMATIONS OF DISCRETE PLANE CURVES

Abstract: Abstract. We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms of the τ function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.

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Cited by 25 publications
(36 citation statements)
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“…The system of bilinear equations (4.9)-(4.11) are included in the discrete two-dimensional Toda lattice hierarchy [12,17,18,19,20,21,22,23,24]. A typical example of f .…”
Section: Explicit Formulamentioning
confidence: 99%
“…The system of bilinear equations (4.9)-(4.11) are included in the discrete two-dimensional Toda lattice hierarchy [12,17,18,19,20,21,22,23,24]. A typical example of f .…”
Section: Explicit Formulamentioning
confidence: 99%
“…It is noticed that a class of Bäcklund transformations for smooth and discrete plane curves in Euclidean space governed by the modified KdV equation were discussed in [12], which are derived by using the Bäcklund transformations of the potential modified KdV equation.…”
Section: Bäcklund Transformations Of Integrable Curve Flows In Rmentioning
confidence: 99%
“…In [4], Wahlquist and Estabrook [4] provides a systematic method to construct Bäcklund transformations of integrable systems by using the prolongation structure approach. Other effective methods to construct Bäcaklund transformations of integrable systems were also proposed in a number of literatures, see for example [2,[5][6][7][8][9][10][11][12] and many more references.…”
Section: Introductionmentioning
confidence: 99%
“…Differential geometry has a close relationship with the theory of integrable systems. In fact, many integrable differential or difference equations arise as compatibility conditions of some geometric objects …”
Section: Introductionmentioning
confidence: 99%
“…In fact, many integrable differential or difference equations arise as compatibility conditions of some geometric objects. 2 Classical Bäcklund transformations studies focus on the transformation of surfaces that have constant negative curvature in R 3 . For a given surface, we can create a new surface in R 3 through constant negative curvature.…”
Section: Introductionmentioning
confidence: 99%